Below you can see the front-view size comparison of the Nikon 1 V3 and Fujifilm S8200. The Nikon 1 V3 is clearly the smaller of the two cameras. Its body is 12mm narrower, 22 mm shorter and 83 mm thinner than the Fujifilm S8200.
The chart below depicts how two cameras compare with average dimensions of the cameras in their class.